Option price with stochastic volatility for both fast and slow mean-reverting regimes

Qiang Zhang; Jiguang Han; Ming Gao

doi:10.1016/j.crma.2013.05.008

Mathematical Economics

Option price with stochastic volatility for both fast and slow mean-reverting regimes

Presented by: Philippe G. Ciarlet

Qiang Zhang ¹; Jiguang Han ^2,^3,¹; Ming Gao ¹

¹ Department of Mathematics, City University of Hong Kong, Hong Kong
² USTC–CityU Joint Advanced Research Center, Suzhou, China
³ Department of Statistics and Finance, University of Science and Technology of China, China

Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 411-414.

Abstract
Résumé

The Heston model of stochastic volatility has been widely adopted in modern finance, especially in option pricing. Usually, the model can be classified as being in one of two different regimes: the fast mean-reverting regime and the slow mean-reverting regime. Different approximations are needed for each regime. We show a surprising result: the solution in both regimes can be approximated by an identical expression. The predictions of the approximation are in excellent agreement with the numerical solutions of the Heston model in both regimes.

Le modèle de volatilité stochastique de Heston a été largement utilisé dans la théorie financière moderne, en particulier pour déterminer le prix des options. Habituellement, ce modèle peut prendre en compte deux régimes différents : le régime de retour rapide à la moyenne et celui de retour lent à la moyenne. Deux solutions différentes ont été données, selon le régime du modèle. Nous démontrons un résultat surprenant : les deux solutions peuvent être approchées par une formule identique. Dans chaque régime, les prédictions de lʼapproximation sont très proches des solutions numériques du modèle de Heston.

Received: 2013-05-03
Accepted: 2013-05-23
Published online: 2013-05-01

DOI: 10.1016/j.crma.2013.05.008

Author's affiliations:

Qiang Zhang ¹; Jiguang Han ^{2, 3, 1}; Ming Gao ¹

¹ Department of Mathematics, City University of Hong Kong, Hong Kong
² USTC–CityU Joint Advanced Research Center, Suzhou, China
³ Department of Statistics and Finance, University of Science and Technology of China, China

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     author = {Qiang Zhang and Jiguang Han and Ming Gao},
     title = {Option price with stochastic volatility for both fast and slow mean-reverting regimes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {411--414},
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     year = {2013},
     doi = {10.1016/j.crma.2013.05.008},
     language = {en},
}

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Qiang Zhang; Jiguang Han; Ming Gao. Option price with stochastic volatility for both fast and slow mean-reverting regimes. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 411-414. doi : 10.1016/j.crma.2013.05.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.05.008/

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[3] Jiguang Han; Ming Gao; Qiang Zhang; Yutian Li Option prices under stochastic volatility, Appl. Math. Lett., Volume 26 (2013) no. 1, pp. 1-4

[4] Steven L. Heston A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud., Volume 6 (1993) no. 2, pp. 327-343

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